Resistance Prediction for Asymmetrical Configurations of High-Speed Catamaran Hull Forms

Transcription

1 Resistance Prediction for Asymmetrical Configurations of High-Speed Catamaran Hull Forms by Srikanth Asapana Bachelor of Technology Naval Architecture and Ocean Engineering Indian Maritime University 2013 A thesis submitted to the College of Engineering at Florida Institute of Technology in partial fulfillment of the requirements for the degree of Master of Science In Ocean Engineering Melbourne, Florida December 2015

2 COPYRIGHT In presenting this thesis in partial fulfillment of the requirements for an advanced degree at the Florida Institute of Technology, I agree that the library shall make it freely available for reference and study. I further agree that permission for copying of this thesis for scholarly purposes may be granted by the Head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Srikanth Asapana Department of Marine and Environmental Systems Florida Institute of Technology Melbourne, Florida Nov 23 rd, 2015 Copyright 2015, Srikanth Asapana All Rights Reserved Signature

3 We the undersigned committee here by approve the attached thesis Resistance Prediction for Asymmetrical Configurations of High-Speed Catamaran Hull Forms by Srikanth Asapana Prasanta K. Sahoo, Ph. D. Hamid Hefazi, Ph. D. Associate Professor Department Head Professor Ocean Engineering Mechanical and Aerospace Engineering Committee Chair Ronnal Reichard, Ph.D. Thomas. D. Waite, Ph. D. Professor Department Head Professor Marine and Environmental Systems Marine and Environmental Systems

4 Resistance Prediction for Asymmetrical Configurations of High- Speed Catamaran Hull Forms by Srikanth Asapana Academic Advisor: Prasanta K. Sahoo (Ph.D) ABSTRACT Predicting the resistance of a high-speed catamaran has been of interest to naval architects for the last three decades. Even though considerable amount of research has been carried out in this area, there remains a degree of uncertainty in the accurate resistance prediction of catamaran hull forms in the early design stage. Researches carried out so far have generally ignored the resistance characteristics of unconventional and unsymmetrical catamaran hull forms. This thesis attempts to undertake a comparative analysis of resistance characteristics between newly developed unconventional catamaran hull forms of different configurations derived from existing conventional NPL series of round bilge catamaran hull forms (Molland et el 1991). For this a set of catamaran hull forms with the main hull length of 1.6 m, and with a different range of slenderness ratio (L/ 1/3 ), B/T ratio are generated by using standard modelling software. The resistance analysis had been carried out by using slender body theory and by using STAR CCM+, a CFD package for Froude numbers 0.25, 0.3, 0.6, 0.8 and 1 respectively and with different separation ratios (s/l) of 0.3 and 0.4. The main objective was to perform a comparative analysis for a wide parameter space which would be encompassing different unconventional hull configurations against conventional hull forms. Literature survey establishes that there is scant literature in public domain to perform resistance analysis on unconventional catamaran hull forms. iii

5 As this is not feasible due to lack of data in areas that were considered crucial, separate resistance analysis will be carried out for each hull configuration. The new resistance analysis is proposed for a broad range of geometrical parameters especially for asymmetrical hulls so that a designer will be able to make a decision regarding powering prediction in the design stage. Finally, the compared resistance results will attempt to conclude whether unconventional and unsymmetrical catamaran hull forms are more efficient than the conventional hull forms. The results obtained from this analysis shows that asymmetrical catamaran hull forms irrespective of the separation ratio outperformed the normal catamaran hull forms at higher Froude number. But there still lies a conspiracy about the resistance characteristics among the Froude number ranging between which is typically a transition range for high-speed. A finer analysis on the range of Froude number should be carried out in obtaining a closer look over the fluctuation of the resistance at high-speed transition range. It is expected that this study would help to provide a foundation in obtaining greater insight regarding resistance characteristics of unconventional catamaran hull forms especially with regard to slenderness ratio (L/ 1/3 ), separation ratio (s/l) and interference effects between the demi-hulls. The conclusions would be beneficial to any early stage designer whose interest lies in advancing the catamaran studies. iv

6 Table of Contents List of Figures vii List of Tables. x List of Abbreviations... xii List of Symbols... xiii Acknowledgement. xv Dedication...xvi CHAPTER INTRODUCTION BACKGROUND CHAPTER THEORY FLOW ANALYSIS OVER CATAMARAN SIDE FORCE VISCOUS EFFECTS COMPONENTS OF TOTAL RESISTANCE STAR-CCM CHAPTER MODEL DEVELOPMENT CONFIGURATIONS OF ASYMMETRICAL CATAMARAN MODELS SLENDER BODY HULL FORMS GEOMETRY 31 v

7 3.4 MESH GENERATION BOUNDARY CONDITION AND SOLUTION SETUP...35 CHAPTER VALIDATION OF CFD 37 CHAPTER CFD ANALYSIS OF ASYMMETRICAL CATAMARAN CFD SIMULATION FORM FACTORS OF ASYMMETRICAL CATAMARAN TOTAL RESISTANCE OF ASYMMETRICAL CATAMARAN.48 CHAPTER CONCLUSION CONCLUSION FUTURE WORK 55 REFERENCES.. 56 APPENDIX A: HYDROSTATICS OF CATAMARAN MODEL 59 APPENDIX B: DATA ON CFD INVESTIGATION. 61 vi

8 List of Figures Figure 1: Wigley catamaran hull 4 Figure 2: Comparison of CW of catamaran at different separation ratios. 5 Figure 3: Series of semi displacement catamaran round bilge hull forms... 7 Figure 4: Zonal distribution of the flow around the hull... 8 Figure 5: Comparison of CW for different series 9 Figure 6: Comparison of total resistance among different methods-first model.10 Figure 7: Comparison of total resistance among different methods-second model Figure 8: Comparison of total resistance among different methods-third model Figure 9: Comparison of statistical methods and the model data Figure 10: Symmetrical catamaran Hull form Figure 11: Asymmetrical catamaran hull form 13 Figure 12: Represent the CT values of an asymmetrical catamaran for corresponding Froude numbers Figure 13: Model 3b body plan, Molland (1994). 25 Figure 14: Body plan of Outboard Asymmetrical Catamaran (s/l-0.3).. 26 Figure 15: Plan view of outboard asymmetrical catamaran (s/l-0.3). 26 vii

9 Figure 16: Body plan view of an inboard Asymmetrical Catamaran (s/l-0.3) 27 Figure 17: Plan view of an inboard Asymmetrical Catamaran (s/l-0.3). 27 Figure 18: S-NPL Lines Planes [Molland et al. (1994)].. 29 Figure 19: Profile view of a Catamaran model 3b (s/l-0.3).30 Figure 20: Plan view of a catamaran (s/l-0.3)..30 Figure 21: Body plan view of a catamaran (s/l-0.3).31 Figure 22: Geometry of Inboard Asymmetrical Catamaran (s/l-0.4).. 32 Figure 23: Geometry of Outboard Asymmetrical Catamaran (s/l-0.4) Figure 24: The domain of catamaran Figure 25: Trimmed cell mesh of catamaran CFD domain (Symmetry).. 35 Figure 26: Comparison of total resistance coefficients [3b mono-hull] Figure 27: Comparison of total resistance coefficients [Catamaran (s/l-0.4)] 39 Figure 28: Comparison of total resistance coefficients [Catamaran (s/l-0.3)].40 Figure 29: Free surface wave contours at Fn 0.6 [3b mono-hull model].. 40 Figure 30: Free surface wave contours at Fn 0.6 [Catamaran (s/l-0.4)].. 41 Figure 31: Two interacting phases [air and water] 42 Figure 32: Contour of pressure layers.. 43 Figure 33: Convergence of Residual Scales viii

10 Figure 34: Free surface wave contours of Inboard Asymmetrical Catamaran (s/l- 0.4) at Fn Figure 35: Free surface wave contours of Outboard Asymmetrical Catamaran (s/l-0.4) at Fn Figure 36: Total resistance coefficients of Asymmetrical catamaran hull [s/l=0.4] Figure 37: Total resistance coefficients of Asymmetrical catamaran hull [s/l=0.3]..46 Figure 38: Total resistance coefficients of Asymmetrical catamaran hull.46 Figure 39: Resistance components [Molland et al. (2011)]...47 Figure 40: Prohaska plot [Molland et al. (2011)] 48 Figure 41: Comparison of total resistance [Inboard Asymmetrical (s/l-0.3)]...51 Figure 42: Comparison of total resistance [Inboard Asymmetrical (s/l-0.4)] 51 Figure 43: Comparison of total resistance [Outboard Asymmetrical (s/l- 0.3)].52 Figure 44: Comparison of total resistance [Outboard Asymmetrical (s/l- 0.4)].52 ix

11 List of Tables Table 1: Parameters of different round bilge models... 7 Table 2: Tested separation and stagger conditions Table 3: Viscous form factor for symmetrical and asymmetrical catamarans for different separation ratios Table 4: Hydrostatics of 3b Asymmetric Catamaran Model [S/L 0.3].. 27 Table 5: Systematic series of round bilge S-NPL models [Molland et al. (1994)] Table 6: Particulars of Catamaran Models Table 7: Trimmed cell mesh details for asymmetrical catamaran model..34 Table 8: Fluid properties of fresh water 35 Table 9: Boundary condition and solution method 36 Table 10: Total resistance coefficients [3b mono-hull].38 Table 11: Total resistance coefficients [3b Catamaran (s/l-0.3)] 38 Table 12: Total resistance coefficients [3b Catamaran (s/l-0.4)].38 x

12 Table 13: Total resistance coefficients of Asymmetrical Catamaran Table 14: The calculated resistance coefficients of Inboard Asymmetrical (s/l- 0.3)...49 Table 15: The calculated resistance coefficients of Inboard Asymmetrical (s/l- 0.4).49 Table 16: The calculated resistance coefficients of Outboard Asymmetrical (s/l- 0.3).50 Table 17: The calculated resistance coefficients of Outboard Asymmetrical (s/l- 0.4).50 Table 18: Form factors of Catamaran Hull models xi

13 List of Abbreviations CAD CFD IGES ITTC NPL NURBS RANS VOF WSA Computer-Aided Designing Computational Fluid Dynamics Initial Graphics Exchange Specification International Towing Tank Convention National Physics Laboratory Non-Uniform Rational B-Splines Reynold s Averaged Navier-Stokes Volume of Fluid Wetted Surface Area xii

14 List of Symbols A B/T C CA CAA CB CF CM CP CT CTcat CV CW CWcat CWdemi F Fn k L L/ 1/3 L/B Area Breadth to Draft ratio Critical coefficient of model Incremental Resistance Coefficient Air Resistance Coefficient Block Coefficient ITTC ship-model correlation line Mid-ship Coefficient Total Pressure Coefficient Total Resistance Coefficient Coefficient of Total Resistance of Catamaran Total Viscous Resistance Coefficient Total Wave Resistance Coefficient Coefficient of Wave Resistance of Catamaran Coefficient of wave resistance for demi hulls Force Froude Number Turbulent Kinetic Energy Length Slenderness Ratio Length to Breadth ratio xiii

15 LCB m R/L Rn RT/ RW S s/l V (1+ K) (1+k) t Longitudinal Center of Buoyancy Mass Stagger Ratio Reynold s Number Total Resistance to Displacement ratio Total Wave Resistance Wetted Surface Area Separation Ratio Velocity Density Dissipation Rate Pressure field change factor Velocity increment factor Viscous Resistance Interference Factor Wave resistance interference factor Form factor for catamaran Form factor for mono hull Turbulent Viscosity xiv

16 Acknowledgement I would like to express my appreciation to Dr. Prasanta Sahoo who read my numerous revisions and for his useful critiques, for being constant inspiration and showing me the lead in this path. He has been so generous and patient during this process. I would also thank Dr. Waite, Dr. Hefazi and Dr. Reichard for spending their valuable time. I would like to extend my sincere thanks to my Naval Architecture laboratory fellow mates for being with me in all the tough times and helping me out in achieving this. xv

17 Dedication To my mother and father xvi

18 Chapter 1 Introduction Though the maritime industry is setting a broad exposure in ship designing through advanced technologies and varying simulation software, the research seems to be never ending in producing finer and optimized design of the vessels. When most of the vessels in the maritime industry are dominated by the conventional mono hull design with distinguishing shapes for desired commercial purposes there is always space available for multi-hull vessels when stability and hydrodynamic performance are considered as the main criteria. Due to rapid development of the high-speed ship market in the past decade, multihulls are considered as the best option to be used in naval and recreational purposes where performance of the vessel could have a profound effect. Hydrodynamic performance is an important aspect to be taken into consideration as it has direct impact on the operational costs. So, at an early stage a designer need to be aware of finding the best possible method which determines or sets a compromise between vessel shape and operational costs to get the desired performance. Though the theoretical approach of hull resistance is complex in nature, it seems economically feasible when compared to model test evaluation. This justifies the effort involved in studying many different theoretical methods in order to evaluate hull resistance properly (Moraes et al 2004). In ship building industry, the catamaran design provide many advantages such as speed, stability and carrying capacity. In general, catamaran hull forms have already proved to be good enough in providing double the deck space even after meeting all the requirements such as stability and performance. Although there is an increase in frictional resistance due to increased wetted surface (demi hulls) area, the effect can be negotiated once the design hull reaches sufficient speed. 1

19 Though interference between the waves hardly affects the resistance of the hull it can be reduced by the optimized design of hull shape (Bertram, (2002); Schneekluth and Bertram, (2002); Larsson and Baba, (1996); White, (1991)). However, finding the resistance and interactive forces between the demi hulls still remained as significant design challenges. The size and shape of the demi hulls have an impact on resistance as well as on interference of the vessel. Whereas all the above points are applicable to all existing catamaran hull forms, in this research an attempt has been made to figure out a new approach of optimizing resistance characteristics of a catamaran by making a significant change in the hull forms which are way different from the existing designs. For example, each demi hull of the catamaran is sliced into half which makes the whole wetted surface area of a catamaran to be half of the conventional catamaran hull form. The design would readily exhibit the decreased viscous resistance that will be experienced by the hulls. Finally the resistance analysis of these different hull configurations are compared to the results of conventional catamaran hulls to arrive at a conclusion that if these configurations are reliable and efficient than the conventional catamaran hull forms. 1.1 Background The concept of multi-hull is known to the mankind since the ages of sailing. The Polynesians are the first to represent the catamaran hull form in 16 th century. But it took two centuries past to have a scientific look over the pros and cons of catamaran hull design. Speed is the main parameter which resulted in the evolution of multi-hull from the conventional mono hulls as the mechanical propulsion came into big picture. In case of mono hulls the high-speed is achieved by a finer hull which exhibits minimum drag characteristics. A slender hull with high L/B ratio would serve the purpose. 2

20 This initiated the need of second hull as a supporting structure which led the innovation of catamaran hulls without a compromise between speed and stability of the vessel. As the twin hulls are finer and exhibits stability efficiency as well as desired speed more than the conventional mono hull design, the researchers have always been interested in the optimized design of the hull to get the desired hydrodynamic performance. Hence, by taking speed as the main aspect there is no doubt that most of the catamarans belongs to the family of high-speed crafts and ferries rather than commercial vessels. When good performance is the output needed from a hull design one should have a great insight in the reduction of resistance characteristics of the hull. Since the catamaran has twin hulls which represents more wetted surface area would also experience more drag characteristics. Also the resistance experienced at slow speeds is much greater when compared to any other conventional mono hulls. There are many model experiments and researches conducted in evaluating the resistance characteristics of the catamaran hull forms. Moraes et al (2003) have investigated on the wave resistance components of the catamaran at different separation ratios (s/l). The authors have performed this investigation using two different methods namely slender body method as postulated by Mitchell 1898 and 3D method based on potential theory used by SHIPFLOW computational method. In the end results from the above two methods are compared to the experimental results of Millward (1992) in order to check the consistency. Wigley hull geometry is used to carry out this investigation. Wigley hull is a parabolic hull form proposed by Wigley (1942) and is one of the most widely tested hull form in the ship design. The equation for a nondimensional wigley hull form is given as (1) and the hull form is shown in figure 1. Y = [± 1 b(1 2 4x2 ) (1 z2 d 2)] 1 x 1, d z 0 (1) 2 2 3

21 This hull geometry is tested for three different separation ratios values say s/l = 0.2, 0.4 and 1 and the results are plotted. The results show similar trade routes by every method but by allowing a little inconsistency (higher) in the wave coefficient (Cw) values by 3-D SHIPFLOW method at Froude number between Figure 1: Wigley Catamaran Hull [Moraes et al (2003)] This difference in the values is justified by the fact that ship flow software utilizes 3D method and takes into account of the hull interference in this particular Froude number range whereas slender body theory and the Millward (1992) case study is based on 2D methodology, Moraes et al (2004). 4

22 Figure 2: Comparison of C W of catamaran at different separation ratios The obtained CW values for other Froude number s ( & 0.75 and above) nearly corresponds to the values given by Millward (1992). Comparison of CW of catamaran at different separation ratios is shown in the Figure 2. The shape of a symmetrical catamaran has a negligible effect on the wave resistance experienced by the catamaran hull (Chengyi 1994). The above plots show that the coefficient of wave resistance peaks at lower Froude numbers ( ) irrespective of the spacing between the hulls. Also as the separation ratio increases the difference in the Cw values given by the 3D SHIPFLOW software and the slender body theory shows a decline in the value which is a phenomena of interference effect. A catamaran hull exhibits a typical tendency in interference corresponding to the Froude numbers. The interference becomes almost zero at lower Froude numbers say below 0.3 and also represents negative interference above Froude number 0.7 Millward (1992). (Chengyi 1994) also proposed that the hull interference which is responsible for the reduction in resistance characteristics occurs at Froude number greater than 0.5 which supports the statement given by Millward (1992). 5

23 Another research has been carried out by Sahoo et al (2007) which primarily focused on the calm water resistance characteristics of a series of semi displacement catamaran of round bilge hull forms. A regression equation has been established for evaluating the resistance characteristics for a wide range of parameters. Though the equation doesn t comply with some of the experimental data and also other factors being uncertainties to some extent, the results yielded provide a considerable promise over using the regression equation (Sahoo et al 2007). This research also includes the discussion over different methods of estimating the wave resistance characteristics but by having the validation of results between the models used and Molland et al (1994) as the top priority. The total resistance of a vessel can be divided into two main components namely viscous resistance and wave making resistance. Viscous resistance can be readily found out from ITTC-1957 ship-model correlation line with the help of a form factor whereas the wave making resistance is an inconceivable factor till date. With the advent in technology and simulation software s there is a likelihood of obtaining the results which are almost accurate but the accurate result is always unpredictable. In this paper the authors used a computational package SHIPFLOW for generating the wave making resistance data for catamaran hull forms and the regression equation has been generated based on the wave data. Later, the extent of validity of the equation is carried out by comparing the results with some experimental methods. For this resistance analysis the authors used a series of round bilge catamaran hull forms which are prominently used by the Australian high speed ferry industry. The analysis has been conducted for a separation ratio (s/l) between 0.2 and 0.4 whereas the speed range is confined to Froude number The round bilge models used are represented in Figure 3. 6

24 Figure 3: Series of semi displacement catamaran round bilge hull forms [Sahoo et al (2007)] This software splits the whole flow around the vessel into three different zones where the appropriate flow equations can be formed and then computes the wave resistance coefficient by summing up all the equations. The flow around the model is basically divided into three zones namely potential flow, boundary layer and turbulent flow. The parameters of the different models are presented in the Table 1. Table 1: Parameters of different round bilge models [Sahoo, Browne, and Salas (2004)] Model L/B B/T CB L/ 1/

25 This research has been limited to perform the resistance characteristics to certain range of Froude number (<1) due to flaws in the computational software being unable to model wave breaking phenomena when Froude number exceeds 1. As the wave resistance coefficient is dependent on number of iterations, ensure that the process runs through decent number of iterations while analyzing. Two types of solvers Linear and Non-linear exist in the SHIPFLOW for running the analysis which obtains wave resistance coefficient. If nothing is specified, the software choses the linear type of solver by default but for achieving accurate results nonlinear type of solver is always recommended. The only drawback with the nonlinear solver is it is unstable particularly at high speeds. Regions based on the flow around the hull are shown in Figure 4. Figure 4: Zonal distribution of the flow around the hull The regression equation of Cw established by the authors for a catamaran demi hull is follows as equation (1). C Wdemi = e c1 ( L B )C2 ( B T )C3 (C C4 B ) ( L C5 1 (i E 3) C6 )( ) C7 ( s L )C8 (1) Three models from the series exhibited the results in conjunction with the results of Molland et al (1994) and it showed a good correlation between the models especially when the Froude number is above 0.5. The comparison of wave coefficient CW for different series of round bilge hull forms is shown in Figure 5. 8

26 Figure 5: Comparison of C W for different series The authors have extended their research in order to sort out the best results on wave resistance characteristics and to obtain more promising nature about the regression equation which is formulated in the first part. A comparative analysis is made on the resistance characteristics in order to validate the accuracy and efficacy of different resistance prediction methods that are used in part 1. A relatively old computational package CATRES which is based on thin ship theory have been used in this research for comparison of the results. The validation of the regression equations developed earlier is done by conducting the resistance analysis experimentally to three most widely used models from the high speed ferry industry. The results obtained from towing tests were non-dimensionalised so that these could be presented and compared with the regression models developed in part 1 of this study (Sahoo et al, 2007). The resistance graphs from different methods chosen are then plotted against different Froude numbers for all the three selected models. 9

27 The Figure 6 below show results of the first model, the computational software CATRES exhibits appropriate results with the experimental data proving the accuracy and dependency levels of the software. On the other hand the regression equation formulated from Ship flow by Sahoo et al (2007) predicts more resistance than experimental data and method implemented by Pham et al (2001) and Sahoo et al (2004) complies with the experimental data though it slightly under predicts the results. Figure 6: Comparison of total resistance among different methods-first model The results of the second model are plotted in the Figure 7. The resistance experienced by this model is higher as can be seen from the values of towing tank results. From the figure below, the experimental data exhibits an increment in linear nature to which the values generated from Ship flow by Sahoo et al (2007) display relatively close results though they are under predicted. CATRES result does not match the towing tank data for a Froude number up to 2. It failed to exhibit the similar trend curve just like any other methods applied as it under predicts the resistance values once crossing the Froude number value

28 Figure 7: Comparison of total resistance among different methods-second model The results (Figure 8) from the CATRES exhibit similar results by over predicting the experimental data. The results from Ship flow by Sahoo et al (2007) produce relatively close results to that of towing tank tests slightly over predicting. Although the results from Sahoo et al (2004) and Pham, Kantimahanthi and Sahoo (2001) seems sufficiently accurate, though it under predicts the experimental data over the speed range. Figure 8: Comparison of total resistance among different methods-third model 11

29 The resistance curves from different methods have exhibited similar trend when compared to the experimental data. Though there is difference which can be seen in resistance curves between methods for a particular vessel and also when compared to different vessels, one must also remember the regression equations are formulated in part 1 are based on a systematic series of hull forms which are different from the three random hulls that are analyzed in this study. As the regression equations tend to show near accuracy in the results, one should also remember that the hull forms used for the regression equations are different from the randomly selected hull forms which are used for obtaining the experimental data and the best results is always expected provided more study and research involving in refining the regression equations. Sampson et al (2005) conducted power prediction analysis on a semi displacement catamaran using a series of comprehensive model tests. The separation ratio of the model tested in this paper is 0.09 thus taking the venturi effects into consideration. These unconventional hull forms have good impact in stability and more efficient while the hull is in planning mode. However, the vessel experiences a lot of resistance during its semi-displacement and displacement mode due to interference effects and relatively higher half angle of entrance which creates significant wave shoulders when compared to conventional catamaran hull forms. An asymmetric demi hull shows significantly less resistance at Froude number more than 1 when compared with the symmetrical catamaran, Fry et al (1972). Whereas asymmetric catamaran exhibits an improved resistance characteristics than demi hull when the Froude number is over At a Froude number range of 0.9, the flow between the demi hulls is smooth without any disturbance but the flow on the outside is associated with large waves which indicates dependency on the half angle of entrance which causes shoulder wave system. Later, the results from the model tests have been compared with different statistical methods in order to validate the efficacy. 12

30 Figure 9 represents the comparison of model data to the statistical methods used and shows that Savitsky method is under predicting the model test data whereas VWS is defining the upper region of the graph. Figure 9: Comparison of statistical methods and the model data (Sampson et al, 2005) Utama et al (2011) have undertaken rigorous testing over the drag characteristics and interference effects between laterally separated and longitudinally staggered catamaran configurations for both symmetrical and asymmetrical hull crosssections. Figure 10 and 11 representing the symmetrical and asymmetrical configuration of catamarans respectively. Figure 10: Symmetrical catamaran Hull form [Utama et al (2011)] Figure 11: Asymmetrical catamaran hull form [Utama et al (2011)] 13

31 The experiments were conducted for Froude number up to 0.7 with three separation hull distances and four longitudinally hull staggers, including the single demihull cases for both symmetrical and asymmetrical hull forms. The test conditions for both hull forms are outlined in Table 2. Also the viscous form factor (1+ k) obtained for symmetrical and asymmetrical catamaran hull forms at different separation ratios and different stagger positions is represented in table 3. Table 2: Tested separation and stagger conditions (Utama et al, 2011) Model Description Separation Ratio (s/l) Stagger (R/L) Demi Hull - - Catamaran 0.2 0,0.2,0.3,0.4 Catamaran Catamaran 0.4 0,0.2,0.3,0.4 Table 3: Viscous form factor for symmetrical and asymmetrical catamarans for different separation ratios (Utama et al, 2011) Hull Form Monohull (1+k) s/l=0.2 s/l=0.3 s/l=0.4 (1+ k) (1+ k) (1+ k) Sym. Catamaran R/L= R/L= R/L= Asym. Catamaran R/L= R/L= R/L=

32 The coefficient of total resistance (CT) values for asymmetrical catamaran hull forms for different separation ratios are plotted in Figure 12. Figure 12: Represent the C T values of an asymmetrical catamaran for corresponding Froude numbers. The research concluded that, although a longitudinally staggered hull design is not immediately practical, their experimental results indicate that as hull separation and stagger are increased, resistance decreases. Furthermore, asymmetrical hulls are found to be less influenced by the interference between hulls than are symmetrical hulls. 15

33 CHAPTER 2 THEORY For high speed applications the asymmetric catamaran hull form shows promise (Sampson et al, 2005). Predicting the resistance characteristics of a ship have always been a difficult task as it is associated with the three prominent factors namely accuracy, time and the application cost. There are two basic ways of predicting the wave resistance which the present world follows. Towing tank test: This method is considered to be the most promising method which yields the accurate resistance results by using the geometrically similar models for testing. The objectives of measurement in resistance towing tank tests are to obtain the relationship between residuary resistance coefficient and Froude number of a ship model and, if required, the form factor. The direct measurement of the tests is the total resistance as well as the running attitudes of a ship model at each speed. CFD method: This is a numerical simulation of the model which behaves just like numerical towing tank and predicts the resistance data. The time period for a completing a simulation is based on the parameters of the model, other attributes and conditions which would be given as input by the user. Although this seems economically feasible when compared to the towing tank test. The prediction of resistance characteristics of an asymmetrical catamaran hull forms can be done by several ways. Extrapolation from geometrically similar models Dedicated model tests Series data based on systematic model tests 16

34 Regression based procedures Computational fluid dynamics The accuracy levels of the different methods decline in the provided order for wellestablished conventional hull forms. Since the availability is so scarce for the resistance data of asymmetrical catamaran hull forms thus it is recommended to go for dedicated model tests and then extrapolate the model results to actual size of the vessel in order to acquire the best possible resistance data. Resistance is the driving force which is responsible for the uniform rectilinear motion of the ship with a constant speed in a calm sea. The total resistance is divided into two components namely viscous resistance which is associated with the friction experienced by the body with respect to the medium, and the other is wave making resistance which causes the generation of waves and nonetheless other associated components. The wave making resistance is the resultant force caused by the pressure changes due to atmosphere on the free surface, which causes waves on the surface. As the speed of ship has profound effect on wave making resistance which eventually increases the total resistance experienced by the ship it is essential to find out ways in reducing it so that better performance of any hull form is achieved. Generally, to do this, high values of L/ 1/3, or increasing the dynamic lift of the hull, are required. Wave making resistance is also affected by the interference between the separate hull wakes. Indeed the favorable wave interference can compensate for the increase of the wetted surface, ensuring the advantages of very slender hulls over a significant range of Froude numbers together with good stability characteristics. 17

35 2.1 Flow analysis over catamaran The flow about a catamaran is symmetric with respect to the center line but not the flow around the demi hulls. The flow irregularity is due to a new effect that arises between the demi hulls widely known as wave interference effect which is also a factor for the resistance. Although this effect can be calculated accurately with the help of thin ship theory provided the slenderness of the demi hulls is small. Apart from this effect, the catamaran also experience a side force and associated induced drag due to the asymmetric nature of the fluid cross flow between the demi hulls. This side force can be cancelled out by the catamaran hull symmetry but it doubles the induced drag force by combining the forces from the demi hulls and generates more resistance which restricts the forward motion of the vessel. This is one of the reasons why catamarans don t respond to the lift force as much as conventional mono hulls do. The only way to get rid of the induced drag force from the demi hulls is done by ensuring that the demi hulls have minimum angle of attack. 2.2 Side Force Side force increase rapidly as the separation ratio between the demi hulls decreases, Couser et al (1998). As a matter of fact, the side force is directly proportional to the speed of the vessel. Since the catamaran with less separation ratio is more susceptible to faster speeds which helps in domination of relative magnitude of the outward force of the radiated wave system and inward force due to the venture effect together results in the increased side force. 2.3 Viscous Effects In general all the viscous forces of a catamaran is a representation of frictional resistance. But still there lacks an involvement of some other secondary effects such as eddy making, viscous interference and transom effects which might crucially affect the total resistance of the catamaran. Insel et al (1992) made an attempt which considers these effects for a catamaran through modification in the 18

36 demi hull form factor. He tested the demi hull in isolation as well as in the form of catamaran through which he derived the difference in the form factor of demi hull in both isolated and also in conjunction with the catamaran. The difference between the two cases is attributed as viscous resistance interference effect (β). This difference when added to the form factor (1+k) of a demi hull introduces a new format of the form factor as (1+ βk). The viscous resistance interference effect mainly comprises of two parts. They are pressure field changes around the demi hulls and the speed increase between the hulls. It depends only on the length to beam ratio of the demi hull and is completely independent on the speed or the separation between the demi hulls. In general, two interference effects contributing to the total resistance effect were found namely viscous interference caused by asymmetric flow around the demi hulls which affects the boundary layer formation and the wave interference due to the interaction of the wave systems produced by each demi hull. 2.4 Components of Total Resistance The ITTC-57 ship-model correlation line (1978) suggested the total resistance components of mono-hull should be expressed by equation (2): CT = (1+k) CF + CW (2) Where (1+k) is the form factor according to Hughes-Prohaska (2008) CF is the frictional resistance coefficient which is always calculated according to the ITTC 57 correlation line and is given by (3): C F = (log 10 R n 2) 2 (3) CW is the wave resistance coefficient and is calculated by the formula (4) CW= R W 1 (4) SV2 2 19

37 Insel and Molland (1992) proposed the total resistance of catamaran was practically expressed by equation (5): C Tcat = (1 + k) C F + τc W (5) Where the factor takes pressure field change around the demi hulls into consideration and the factor takes account of velocity increment between the hulls which can be calculated by simple integration of the local frictional resistance over the wetted surface area. Where τ is the wave resistance interference factor. This equation is much more simplified and given as equation (6) C Tcat = (1 + βk)c F + τc W (6) Where is the viscous interference factor And (1+ k) is the form factor for the catamaran For a catamaran, can be calculated using the following equation = Cw cat Cw demi A satisfactory fit to the catamaran form factors given by Couser et al (1997). (7) (1 + βk) = 3.03 ( L 0.4 1) 3 (8) Also there are other minor components which accounts for the total resistance experienced by the vessel. They are the air resistance experienced by the superstructure of the vessel and the appendage resistance due to the roughness and unevenness of the surface evolved during the construction phase. So, the equation which involves all these terms is given as CT=CW+CF+CA+CAA (9) 20

38 where CA is incremental resistance coefficient taking into account the effect of roughness of the surface of the ship and CAA is the air resistance coefficient. Where as in CFD the total viscous drag is measured as a direct physical measurement of resistance components and is given by equation (10). C T = C V + C P (10) Where CV is viscous resistance coefficient and CP is pressure resistance coefficient. To calculate the total resistance, the wave resistance coefficient is obtained by experimental data (Molland, 1994), and the frictional resistance coefficient is calculated by using the form factor and ITTC 57 correlation line so that the total resistance coefficient can be expressed as (11): C Tcal = (1 + k) C FITTC + C Wexp (11) 21

39 2.5 STAR CCM+ The three basic principles on which the fluid dynamics is dependent on are Conservation of Mass Conversation of Energy Newton s Second Law, F=ma These principles are governed into numerical equations in fluid dynamics and are represented as the equations of continuity, energy and momentum. These are generally called as transport equations or conversation equations. The form of this equations used in CFD is known as Navier-Stokes equations. STAR-CCM+ (2014), a CFD package provides comprehensive modeling capabilities for a wide range of incompressible, compressible, laminar and turbulent fluid flow problems and solves conservation equations of mass an momentum. In this thesis, incompressible, viscous turbulent and two phase (airwater) flow is considered. For this flow the governing equations are written as incompressible Reynolds-averaged Navier-Stokes equation. The CFD package used takes finite volume method to transform the continuous governing equations into a form that can be solved numerically by using segregated solver, where the flow equations are solved one after the other and linked using a correction equation. The volume of fluid model is used in this thesis is exceptionally provided for systems containing two or more unmixable fluid phases, where each phase constitutes a large structure within the system (such as typical free surface flows). This approach captures the movement of the interface between the fluid phases, and is often used for marine applications. A k- turbulence model is a two-equation model in which transport equations are solved for the turbulent kinetic energy k and its dissipation rate 22

40 The two-layer approach, is an alternative to the low-reynolds number approach that allows the k- model to be applied in the viscous sub layer. In this approach, the computation is divided into two layers. In the layer next to the wall, the turbulent dissipation rate and turbulent viscosity t are specified as functions of wall distance. The values of specified in the near-wall layer are blended smoothly with the values computed from solving the transport equation far from the wall. The equation for the turbulent kinetic energy is solved in the entire flow. This approach generally obtain results that are often good or better. The turbulence model used in this analysis is the realizable two-layer k- model for getting better results. This model combines the realizable k- model with the twolayer approach. This model contains a new transport equation for the turbulent dissipation rate. Also, a critical coefficient of the model, C is expressed as a function of mean flow and turbulence properties, rather than assumed to be constant as in the standard model. The realizable k- model is substantially better than the standard k- model for many applications, and can generally be relied upon to give answers that are at least as accurate. For Eulerian multiphase cases, where more than one phase exists the turbulence kinetic energy k, and its rate of dissipation,, are given by following transport equations (12) and (13).. d dt α iρ i k i dv + V α i ρ i k i (v v g ). da = α i (μ + μ i ) k σ i da + α i [f c 1 G k i + G b i A A k V ρ i ((ε i ε 0 ) + Y i M ) + S i k + S i kr ] dv + (m ij k j (ij) mji k i ) i=1 (12).... d dt α iρ i ε i dv + V α i ρ i ε i (v v g ). da = α i (μ + μ i ) σ i. da + α i [f c 1 C 1 S + A A V.. ε i K i (C 1 C 3 G i b ) ε i k i + vε i C 2 ρ i (ε i ε 0 ) + S i + S r (ij) i ] dv + i=1 (m ij ε j mji ε i ) (13) 23

41 Where V is the cell volume, α i is the volume fraction of phase i and being the density The turbulent viscosity is computed for two layer approach is given by the expression (14) and (15) t = y v y 1.6 (14) v Where y v = Re y 2 k (15) 2 k = Re y Re y Re y 3 24

42 CHAPTER 3 MODEL DEVELOPMENT A catamaran comprises of two demi hulls usually with each demi hull having the same waterline length and breadth. They are usually positioned parallel to each other with a certain distance between the center lines of each hull which is termed as separation ratio (s/l). This research deals with the comparison of resistance characteristics between newly created asymmetrical catamaran hull forms and those with existing S-NPL series round bilge catamaran hull forms. The mono hull model was initially chosen from the series of S-NPL round bilge hull forms of Molland et al. (1994). The hull model 3b is used as parent hull in creating different configurations of asymmetrical catamarans and is shown in Figure 13. Figure 13: Model 3b body plan, Molland (1994) 3.1 The Configurations of Asymmetrical Catamaran model Two models of asymmetrical catamarans namely Inboard Asymmetric and Outboard Asymmetric catamaran hull forms are created from the existing S-NPL series mono hull model 3b with two different separation ratio (s/l) between the 25

43 demi hulls as 0.3 and 0.4. The asymmetrical demi hull is arranged such that the hull width is a half of the symmetrical hull with the flat sides facing inwards and outwards. Based on S-NPL systematic series, the models were generated by using Maxsurf Modeling software, which is a standard modelling software. The hulls are transformed into closed poly surface, a solid body with the help of Rhinoceros 5, a CAD software before implementing the resistance analysis. Figure 14: Body plan view of an Outboard Asymmetrical Catamaran (S/L-0.3) Figure 15: Plan view of an Outboard Asymmetric Catamaran (s/l-0.3) 26

44 Figure 16: Body plan view of an inboard Asymmetrical Catamaran (s/l-0.3) Figure 17: Plan view of an inboard Asymmetrical Catamaran (s/l-0.3) Table 4: Hydrostatics of 3b Asymmetric Catamaran Model [s/l 0.3] Parameter Value Units Displacement 16.7 Kg Draft m Wetted Surface Area m 2 CB L/B B/T L/ 1/

45 3.2 Slender Body Hull Forms Resistance data has been established for a systematic series of round bilge displacement hull forms from the towing tank experiments conducted in the National physics laboratory by Molland et al (1994). 22 models have been tested by varying L/B and B/T ratios. Molland et al. (1994) predicted wave making resistance on the systematic series of 10 round bilge NPL hulls for a Froude number ranging The below table represents the models and their nondimensional parameters respectively where the Slenderness ratio L/ 1/3, ranging from 6.27 to As the total resistance is obtained from the towing test results, the residuary resistance is then calculated for every model by subtracting the frictional resistance which is determined from the ITTC correlation line Table 5: Systematic series of round bilge S-NPL models [Molland et al. (1994)] Model L(m) L/B B/T L/ 1 3 CB CP CM WSA (m 2 ) LCB (%) 3b a b c a b c a b c

46 Figure 18: S-NPL Lines Planes [Molland et al. (1994)] 29

47 Table 6: Particulars of Catamaran Models Model LWL (m) Wetted Area (m 2 ) Draft (m) B/T s/l Model 3b , 0.4 Inboard Asymmetric Outboard Asymmetric , , 0.4 Figure 19: Profile view of a Catamaran model 3b (s/l-0.3) Figure 20: Plan view of a catamaran (s/l-0.3) 30

48 Figure 21: Body plan view of a catamaran (s/l-0.3) 3.3 Geometry Generating an extensive CFD solution is must when the results are used to interpret the actual solution for the problem. So, it requires a great attention in setting up and also in the process of analyzation. CFD analysis of a problem involves three main steps namely pre-processing, analysis of the problem and post-processing (Mahmood, 2001). Pre-processing involves creation and importing the model geometry, domain creation, accurate model meshing and setting up all the required conditions. Analysis is done by the CFD program by running the simulations for enormous iterations according to the conditions given in the input by the user. Post- processing starts once the simulation gets over and mainly includes the generation of different graphs and values corresponding to the problem. The asymmetrical catamaran model was initially created as Non-uniform rational B-spline (NURBS) curves using Maxsurf modeler. Then the model is converted to IGES file which can be imported to a CAD software for solid modeling. 31

49 The surfaces are created using Rhinoceros, a CAD program and the model is converted to closed poly surface, a representation of the solid body. The solid bodies of asymmetrical catamaran hull forms can be seen in the Figure 22 and 23 Figure 22: Geometry of Inboard Asymmetrical Catamaran (s/l-0.4) Figure 23: Geometry of Outboard Asymmetrical Catamaran (s/l-0.4) 32

50 Once the model is transformed into a solid body it is imported to the Star CCM+ geometry and the domain is created. The domain is the boundary within which the analysis will be made and also acts as a towing tank where the medium flows for close representation of real world scenario. The domain size is determined by length of the hull, and is taken as one ship length forward and five ships length aft of the main hull. The breadth is created one ship length port and starboard of the main hull. The depth is one ship length in the air and one ship length in the water. The domain of a catamaran hull is shown in Figure 24. Figure 24: The domain of catamaran Any CFD package takes quit long time for a simulation to complete. So, one should have insight about ways available for computational time reduction. Since the model of a catamaran is of symmetric in nature it can be modelled as a half domain along the central longitudinal axis in order to save the computational calculation. 33

51 The domain zones are defined as inlet, outlet, symmetry, top, bottom and side. Inlet is specified at the front of the domain where the fluid inflow happens and outlet is named at the rear of the domain. 3.4 Mesh Generation After the domain is created, Boolean operation is performed to subtract the model from the domain which represents the whole domain as a single body rather than two different parts. The next step is to generate a fine meshing over the created half of the domain. For the accurate mesh the trimmed cell meshing method was used as it allows for a greater mesh quality and obtaining a good result of the marine solution as suggested by the STAR CCM+. Trimmed cell mesh of the half domain for catamaran is shown in Figure 25 and Table 7 representing the meshing details. Table 7: Trimmed cell mesh details for asymmetrical catamaran model Cell/Elements 16,76,114 Faces 20,20,196 Minimum size (m) Maximum size (m) Figure 25: Trimmed cell mesh of catamaran CFD domain (Symmetry) 34

52 3.5 Boundary Condition and Solution Setup In this study the flow simulation of the model is mainly conducted with the commercial software of STAR CCM+. The system is considered as three dimensional steady, incompressible, viscous turbulent flow, and multi-phase flow. The fluid properties of water are given by Table 8. Table 8: Fluid properties of fresh water Kinematic Viscosity, ν 1.005ⅹ10-6 m 2 /s Dynamic Viscosity, E-4 pa-s Density, kg/m 3 The motion of the free surface is governed by gravitational force so does the gravity effects should be taken into account in the boundary conditions. Since volume of fluid (VOF) method is suitable for modelling free surface flows such as ship motion through open water, filling of tank, and sloshing (Jones and Clarke, 2010), VOF formulation is applied in CFD to solve the multiphase free surface flows In order to compute the turbulence flow, there are different turbulence models by default in the CFD package say Standard and Realizable k-ε models. Those turbulence models based on RANS equation have similar forms with transport equation of k andε. However the turbulence model of realizable k-ε two layer method is applied for the computation since it is likely to provide superior performance compared with standard k-ε two layer model for flow involving the boundary layers and accurately predicts the spreading rate of planar. For the real circumstance, multi-phases are chosen for fluid condition, which are defined as air and water. 35

53 The primary phase is set to water which has higher density, while the secondary phase is the air which has the lowest density. The coupling of inlet and outlet is set up for velocity inlet and pressure outlet to calculate the pressure and viscous forces on the free surface ship flow. The boundary condition and solution method used in this study is given by Table 9. Table 9: Boundary condition and solution method Inlet/Outlet Velocity Inlet/Pressure Outlet Turbulence Intensity and Length Scale 0.01%, 0.01m Pressure Velocity Volume Fraction Turbulent Kinetic Energy Field Function Field Function Composite Constant 36

54 CHAPTER 4 VALIDATION OF CFD Power prediction of asymmetrical catamaran hull forms has always been challenging due to lack of data since it is involved with varying hull parameters. To determine the degree to which a model is an accurate representation of the real world from the perspective of the intended use of the model it is important to validate the data from CFD. The S-NPL model 3b has been taken as the parent hull and is converted to Inboard and Outboard asymmetrical catamaran hull forms for which the resistance analysis had been run for different Froude numbers. Since the asymmetrical catamaran hull forms exhibits different displacement value, comparison of the resistance results to the original catamaran 3b hull form of other displacement sounds inappropriate. Therefore the catamaran 3b hull form is processed through a parametric transformation where it meets the same displacement as the asymmetrical catamaran hull forms and thus by making the comparison much easier. The validation is done by performing resistance analysis on both mono hull and catamaran hull form for separation ratio 0.3 and 0.4 of model 3b for the Froude numbers 0.25, 0.3, 0.6, 0.8, 1 and the results are compared to the experimental data which has already been established in ship science report 71. The total resistance coefficient compared with CFD and experimental data for mono-hull and catamaran are given in Table 10, 11 and 12. The results show that the CFD analysis has good agreements with the experimental results, as shown below in Figure 26, 27 and

55 Table 10: Total resistance coefficients [3b mono-hull] Fn 10 3 CT (Experimental) 10 3 CT (CFD) Error % Table 11: Total resistance coefficients [3b Catamaran (s/l-0.3)] Fn 10 3 CT (Experimental) 10 3 CT (CFD) Error % Table 12: Total resistance coefficients [3b Catamaran (s/l-0.4)] Fn 10 3 CT (Experimental) 10 3 CT (CFD) Error %

56 C T 103CT Mono hull - 3b Experimental CFD Fn Figure 26: Comparison of total resistance coefficients [3b mono-hull] Catamaran (s/l-0.4) Experimental CFD F n Figure 27: Comparison of total resistance coefficients [Catamaran (s/l-0.4)] 39

57 Catamaran (s/l-0.3) C T Experimental CFD F n Figure 28: Comparison of total resistance coefficients [Catamaran (s/l-0.3)] The wave contours computed by CFD are illuminated by the volume fraction scheme on the free surface, as shown in Figure 29 and 30 Figure 29: Free surface wave contours at F n 0.6 [3b mono-hull model] 40

58 Figure 30: Free surface wave contours at F n 0.6 [Catamaran (s/l-0.4)] 41

59 CHAPTER 5 CFD ANALYSIS 5.1 CFD SIMULATION As a result of good agreement existing between the CFD results and experimental data for mono hull and catamaran, the asymmetrical catamaran hull forms are processed in Star CCM+ for computing total resistance values. The simulations are carried out in the speed range corresponding to Froude numbers 0.25, 0.3, 0.6, 0.8 and 1 for calculating the total resistance of the asymmetrical catamaran hull forms. Multiphase boundary condition is set up which involves the simultaneous flow of two interacting phases and are defined as air and water as shown in Figure 31. Figure 31. Two interacting phases [air and water] Volume of Fluid (VOF) is a simple multiphase model which can be used for simulating flows of several immiscible fluids possessing a capability of resolving the interface between the phases of the mixture and thus helping in no more extra modeling for inter phase interaction. This also should meet the requirement of each phase taking up large structure of the system itself and is often used in marine applications. 42

60 The turbulence model is set up for realizable k-ε two layer method, and the pressure boundary is chosen for the coupling of inlet and outlet, which involved the turbulence intensity and length scales setup. Particularly in this model, the turbulence intensity is set below 1% for external flow, which is a condition for low turbulence. Figure 32 representing the pressure distribution in the virtual towing tank that is created in CFD analysis. Figure 32: Contour of pressure layers In this study the solver settings are in the pressure-velocity coupling scheme so that simple scheme applies to the VOF models. When the residuals scale is converged, the total resistance of asymmetrical catamaran hull configuration are computed and solved. The residuals scales indicate continuity, k-ε, and velocity scale against iteration, as shown in Figure 33. Figure 33: Convergence of residual scales 43

61 The free surface wave counters of Inboard and Outboard asymmetrical catamaran hull forms for a separation ratio of 0.4 are shown in the Figures 34 and 35 respectively Fig 34: Free surface wave contours of Inboard Asymmetrical Catamaran (s/l-0.4) at F n 0.8 Fig 35: Free surface wave contours of Outboard Asymmetrical Catamaran (s/l-0.4) at F n 1 44